Alex, ben, and carl have some money. if alex gives $4.55 to ben, the two boys will have an equal amount of money. if ben gives $4.55 to alex, alex will have 3 times as much money as ben. carls amount of money is the sum of the two other boys' money. how much do the three boys have in all?

$72.80 Let's create a series of equations to express what we know. I'll use the variables A,B,C to represent respectively Alex's, Ben's and Carl's money. "If Alex gives $4.55 to Ben, the two boys will have an equal amount of money." A - 4.55 = B + 4.55 "If Ben gives $4.55 to Alex, Alex will have 3 times as much money as Ben. A + 4.55 = (B - 4.55)*3 Carls amount of money is the sum of the two other boys' money. How much do the three boys have in all? C = A + B Let's take the 1st equation and solve for A A - 4.55 = B + 4.55 A = B + 4.55 + 4.55 A = B + 9.10 Now let's take the 2nd equation and substitute (B+9.10) for A and then solve for B. A + 4.55 = (B - 4.55)*3 (B+9.10) + 4.55 = (B - 4.55)*3 B + 9.10 + 4.55 = 3B - 3*4.55 B + 13.65 = 3B - 13.65 13.65 = 2B - 13.65 13.65 + 13.65 = 2B 2*13.65 = 2B 13.65 = B So Ben has 13.65. Let's use that to calculate Alex's money. A = B + 9.10 A = 13.65 + 9.10 A = 22.75 And now we know that Alex has 22.75, let's use that and Ben's amount to calculate Carl's C = A + B C = 22.75 + 13.65 C = 36.40 So Alex has $22.75, Ben has $13.65, and Carl has $36.40. Since we're looking for the total amount of money the boys have, that is: $22.75 + $13.65 + $36.40 = $72.80